Asian Journal of Pure and Applied Mathematics

This paper examines the properties of solution of transient mixed convection flow in a vertical micro- annulus with internal heat generation and variable viscosity effects. A mathematical model describing the coupled momentum and energy equations is formulated using Boussinesq approximation and transformed into a non-dimensional form. The existence and uniqueness of the solution are established. The Kolodner–Pederson’s lemma is then employed to examine the qualitative behaviour of the solution. The study establishes that, the mathematical model is well-posed and physically consistent, the fluid velocity \(\phi\)(\(\eta,t\)) and fluid temperature \(\phi\)(\(\eta,t\))are bounded, exhibit thermal stability and evolve monotonically in a predictable manner over time toward finite limiting values. These findings contribute to the theoretical understanding of heat transfer processes in micro-scale annular systems with applications in thermal energy storage, cooling techniques, and engineering heat transfer devices.